The DT-instanton equation on almost Hermitian 6-manifolds

Abstract

This article investigates a set of partial differential equations, the DT-instanton equations, whose solutions can be regarded as a generalization of the notion of Hermitian-Yang-Mills connections. These equations owe their name to the hope that they may be useful in extending the DT-invariant to the case of symplectic 6-manifolds. In this article, we give the first examples of non-Abelian and irreducible DT-instantons on non-Kähler manifolds. These are constructed for all homogeneous almost Hermitian structures on the manifold of full flags in ${\mathbb{C}}^3$. Together with the existence result we derive a very explicit classification of homogeneous DT-instantons for such structures. Using this classification we are able to observe phenomena where, by varying the underlying almost Hermitian structure, an irreducible DT-instanton becomes reducible and then disappears. This is a non-Kähler analogue of passing a stability wall, which in string theory can be interpreted as supersymmetry breaking by internal gauge fields.

28 pages, 2 figures

References in corpus (3)

• Stability Walls in Heterotic Theories
• Deformation theory of nearly Kähler manifolds
• Deformations of nearly Kähler instantons